一类富营养湖泊中藻类的状态反馈控制模型
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摘要
建立了一类具有状态反馈控制的湖泊营养成分与藻类的生态系统.在无脉冲控制系统定性分析结果的基础上,利用微分方程的几何理论研究了所建状态脉冲系统阶1周期解的存在性,并给出了轨道稳定性的条件.
A class of ecological system of lake nutrients and algae with state feedback control was presented.Based on the qualitative analysis results of the system without impulsive control,the existences of order-1 periodic solution about the impulsive system were proved by using the geometric theory of differential equations. The conditions for the orbital stability of order-1 periodic solution were given.
A class of ecological system of lake nutrients and algae with state feedback control was presented.Based on the qualitative analysis results of the system without impulsive control,the existences of order-1 periodic solution about the impulsive system were proved by using the geometric theory of differential equations. The conditions for the orbital stability of order-1 periodic solution were given.
引文
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[2]吴锋,战金艳,邓祥征,等.中国湖泊富营养化影响因素研究——基于中国22个湖泊实证分析[J].生态环境学报,2012,21(1):94-100..
[3]姜永军,丁敏,丁磊.水体富营养化控制因子及其污染途径研究[J].甘肃科技,2003,19(10):91-92.
[4]陈兰荪,宋新宇,陆征一.数学生态学模型与研究方法[M].成都:四川科学技术出版社,2003.
[5]宋新宇,郭红建,师向云.脉冲微分方程理论及其研究[M].北京:科学出版社,2011.
[6]Simeonov P S,Bainov D D.Orbital stability of the periodic solutions of autonomous systems with impulse effect[J].Publ RIMS,Kyoto Univ,1998(25):321-346.
[7]Guo H J,Song X Y,Chen L S.Qualitative analysis of a korean pine forest model with impulsive thinning measure[J].Applied Mathematics and Computation,2014,234:203-213.
[8]陈兰荪.害虫治理与半连续动力系统几何理论[J].北华大学学报:自然科学版,2011,12(1):1-9.
[9]傅金波,陈兰荪.资源与资源利用者的脉冲收获控制[J].生物数学学报,2011,26(4):703-712.
[10]Fu J B,Wang Y Z.The mathematical study of pest management strategy[J].Discrete Dynamics in Nature and Society,2012.DOI:10.1155/2012/251942.
[11]傅金波,陈兰荪.水葫芦生态系统状态反馈控制[J].应用数学,2013,26(1):51-57.